Non-Newtonian fluid

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A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, that is, it has variable viscosity dependent on stress. In particular, the viscosity of non-Newtonian fluids can change when subjected to force. Ketchup, for example, becomes runnier when shaken and is thus a non-Newtonian fluid. Many salt solutions and molten polymers are non-Newtonian fluids, as are many commonly found substances such as custard, [1] toothpaste, starch suspensions, corn starch, paint, blood, melted butter, and shampoo.

Contents

Most commonly, the viscosity (the gradual deformation by shear or tensile stresses) of non-Newtonian fluids is dependent on shear rate or shear rate history. Some non-Newtonian fluids with shear-independent viscosity, however, still exhibit normal stress-differences or other non-Newtonian behavior. In a Newtonian fluid, the relation between the shear stress and the shear rate is linear, passing through the origin, the constant of proportionality being the coefficient of viscosity. In a non-Newtonian fluid, the relation between the shear stress and the shear rate is different. The fluid can even exhibit time-dependent viscosity. Therefore, a constant coefficient of viscosity cannot be defined.

Although the concept of viscosity is commonly used in fluid mechanics to characterize the shear properties of a fluid, it can be inadequate to describe non-Newtonian fluids. They are best studied through several other rheological properties that relate stress and strain rate tensors under many different flow conditions—such as oscillatory shear or extensional flow—which are measured using different devices or rheometers. The properties are better studied using tensor-valued constitutive equations, which are common in the field of continuum mechanics.

Types of non-Newtonian behavior

Summary

Classification of fluids with shear stress as a function of shear rate. Rheology of time independent fluids.svg
Classification of fluids with shear stress as a function of shear rate.
Comparison of non-Newtonian, Newtonian, and viscoelastic properties
Viscoelastic Kelvin material, Maxwell material "Parallel" linear combination of elastic and viscous effects [2] Some lubricants, whipped cream, Silly Putty
Time-dependent viscosity Rheopectic Apparent viscosity increases with duration of stress Synovial fluid, printer ink, gypsum paste
Thixotropic Apparent viscosity decreases with duration of stress [2] Yogurt, peanut butter, xanthan gum solutions, aqueous iron oxide gels, gelatin gels, pectin gels, hydrogenated castor oil, some clays (including bentonite, and montmorillonite), carbon black suspension in molten tire rubber, some drilling muds, many paints, many floc suspensions, many colloidal suspensions
Non-Newtonian Viscosity Shear thickening (dilatant)Apparent viscosity increases with increased stress [3] Suspensions of corn starch in water (oobleck)
Shear thinning (pseudoplastic)Apparent viscosity decreases with increased stress [4] [5] Nail polish, whipped cream, ketchup, molasses, syrups, paper pulp in water, latex paint, ice, blood, some silicone oils, some silicone coatings, sand in water
Generalized Newtonian fluids Viscosity is function of the shear strain rate.
Stress depends on normal and shear strain rates and also the pressure applied on it
Blood plasma, custard, water

Shear thickening fluid

The viscosity of a shear thickening i.e. dilatant   fluid appears to increase when the shear rate increases. Corn starch suspended in water ("oobleck", see below) is a common example: when stirred slowly it looks milky, when stirred vigorously it feels like a very viscous liquid.

Shear thinning fluid

Paint is a non-newtonian fluid. A flat surface covered with white paint is oriented vertically (before taking the picture the flat surface was horizontal, placed on a table). The fluid starts dripping down the surface but, because of its non-newtonian nature, it is subjected to stress due to the gravitational acceleration. Therefore, instead of slipping along the surface, it forms very large and very dense droplets with limited dripping. Painting with non-newtonian fluid.jpg
Paint is a non-newtonian fluid. A flat surface covered with white paint is oriented vertically (before taking the picture the flat surface was horizontal, placed on a table). The fluid starts dripping down the surface but, because of its non-newtonian nature, it is subjected to stress due to the gravitational acceleration. Therefore, instead of slipping along the surface, it forms very large and very dense droplets with limited dripping.

A familiar example of the opposite, a shear thinning fluid, or pseudoplastic fluid, is wall paint: The paint should flow readily off the brush when it is being applied to a surface but not drip excessively. Note that all thixotropic fluids are extremely shear thinning, but they are significantly time dependent, whereas the colloidal "shear thinning" fluids respond instantaneously to changes in shear rate. Thus, to avoid confusion, the latter classification is more clearly termed pseudoplastic.

Another example of a shear thinning fluid is blood. This application is highly favoured within the body, as it allows the viscosity of blood to decrease with increased shear strain rate.

Bingham plastic

Fluids that have a linear shear stress/shear strain relationship but require a finite yield stress before they begin to flow (the plot of shear stress against shear strain does not pass through the origin) are called Bingham plastics. Several examples are clay suspensions, drilling mud, toothpaste, mayonnaise, chocolate, and mustard. The surface of a Bingham plastic can hold peaks when it is still. By contrast Newtonian fluids have flat featureless surfaces when still.

Rheopectic or anti-thixotropic

There are also fluids whose strain rate is a function of time. Fluids that require a gradually increasing shear stress to maintain a constant strain rate are referred to as rheopectic. An opposite case of this is a fluid that thins out with time and requires a decreasing stress to maintain a constant strain rate (thixotropic).

Examples

Many common substances exhibit non-Newtonian flows. These include: [6]

Oobleck

Demonstration of a non-Newtonian fluid at Universum in Mexico City UniversumUNAM55 (cropped).JPG
Demonstration of a non-Newtonian fluid at Universum in Mexico City
Oobleck on a subwoofer. Applying force to oobleck, by sound waves in this case, makes the non-Newtonian fluid thicken. Corn speaker.jpg
Oobleck on a subwoofer. Applying force to oobleck, by sound waves in this case, makes the non-Newtonian fluid thicken.

An inexpensive, non-toxic example of a non-Newtonian fluid is a suspension of starch (e.g., cornstarch/cornflour) in water, sometimes called "oobleck", "ooze", or "magic mud" (1 part of water to 1.5–2 parts of corn starch). [8] [9] [10] The name "oobleck" is derived from the Dr. Seuss book Bartholomew and the Oobleck . [8]

Because of its dilatant properties, oobleck is often used in demonstrations that exhibit its unusual behavior. A person may walk on a large tub of oobleck without sinking due to its shear thickening properties, as long as the individual moves quickly enough to provide enough force with each step to cause the thickening. Also, if oobleck is placed on a large subwoofer driven at a sufficiently high volume, it will thicken and form standing waves in response to low frequency sound waves from the speaker. If a person were to punch or hit oobleck, it would thicken and act like a solid. After the blow, the oobleck will go back to its thin liquid-like state.

Flubber (slime)

Slime flows under low stresses but breaks under higher stresses Pouring Slime.JPG
Slime flows under low stresses but breaks under higher stresses

Flubber, also commonly known as slime, is a non-Newtonian fluid, easily made from polyvinyl alcohol–based glues (such as white "school" glue) and borax. It flows under low stresses but breaks under higher stresses and pressures. This combination of fluid-like and solid-like properties makes it a Maxwell fluid. Its behaviour can also be described as being viscoplastic or gelatinous. [11]

Chilled caramel topping

Another example of non-Newtonian fluid flow is chilled caramel ice cream topping (so long as it incorporates hydrocolloids such as carrageenan and gellan gum). The sudden application of force—by stabbing the surface with a finger, for example, or rapidly inverting the container holding it—causes the fluid to behave like a solid rather than a liquid. This is the "shear thickening" property of this non-Newtonian fluid. More gentle treatment, such as slowly inserting a spoon, will leave it in its liquid state. Trying to jerk the spoon back out again, however, will trigger the return of the temporary solid state. [12]

Silly Putty

Silly Putty is a silicone polymer based suspension that will flow, bounce, or break, depending on strain rate.

Plant resin

Plant resin is a viscoelastic solid polymer. When left in a container, it will flow slowly as a liquid to conform to the contours of its container. If struck with greater force, however, it will shatter as a solid.

Quicksand

Quicksand is a shear thinning non-Newtonian colloid that gains viscosity at rest. Quicksand's non-Newtonian properties can be observed when it experiences a slight shock (for example, when someone walks on it or agitates it with a stick), shifting between its Gel and Sol phase and seemingly liquefying, causing objects on the surface of the quicksand to sink.

Ketchup

Ketchup is a shear thinning fluid. [3] [13] Shear thinning means that the fluid viscosity decreases with increasing shear stress. In other words, fluid motion is initially difficult at slow rates of deformation, but will flow more freely at high rates. Shaking an inverted bottle of ketchup can cause it to transition to a lower viscosity through shear thinning, making it easier to pour from the bottle.

Dry granular flows

Under certain circumstances, flows of granular materials can be modelled as a continuum, for example using the μ(I) rheology. Such continuum models tend to be non-Newtonian, since the apparent viscosity of granular flows increases with pressure and decreases with shear rate. The main difference is the shearing stress and rate of shear.

See also

Related Research Articles

In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (flow) under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear force applied to them.

Rheology is the study of the flow of matter, primarily in a fluid state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is a branch of physics, and it is the science that deals with the deformation and flow of materials, both solids and liquids.

<span class="mw-page-title-main">Ketchup</span> Sauce used as a condiment

Ketchup or catsup is a table condiment with a sweet and sour flavor. The unmodified term ("ketchup") now typically refers to tomato ketchup, although early recipes for various different varieties of ketchup contained mushrooms, oysters, mussels, egg whites, grapes or walnuts, among other ingredients.

A Newtonian fluid is a fluid in which the viscous stresses arising from its flow are at every point linearly correlated to the local strain rate — the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector.

In continuum mechanics, a power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid for which the shear stress, τ, is given by

Hemorheology, also spelled haemorheology, or blood rheology, is the study of flow properties of blood and its elements of plasma and cells. Proper tissue perfusion can occur only when blood's rheological properties are within certain levels. Alterations of these properties play significant roles in disease processes. Blood viscosity is determined by plasma viscosity, hematocrit and mechanical properties of red blood cells. Red blood cells have unique mechanical behavior, which can be discussed under the terms erythrocyte deformability and erythrocyte aggregation. Because of that, blood behaves as a non-Newtonian fluid. As such, the viscosity of blood varies with shear rate. Blood becomes less viscous at high shear rates like those experienced with increased flow such as during exercise or in peak-systole. Therefore, blood is a shear-thinning fluid. Contrarily, blood viscosity increases when shear rate goes down with increased vessel diameters or with low flow, such as downstream from an obstruction or in diastole. Blood viscosity also increases with increases in red cell aggregability.

In materials science and continuum mechanics, viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.

<span class="mw-page-title-main">Thixotropy</span> Change in viscosity of a gel or fluid caused by stress

Thixotropy is a time-dependent shear thinning property. Certain gels or fluids that are thick or viscous under static conditions will flow over time when shaken, agitated, shear-stressed, or otherwise stressed. They then take a fixed time to return to a more viscous state. Some non-Newtonian pseudoplastic fluids show a time-dependent change in viscosity; the longer the fluid undergoes shear stress, the lower its viscosity. A thixotropic fluid is a fluid which takes a finite time to attain equilibrium viscosity when introduced to a steep change in shear rate. Some thixotropic fluids return to a gel state almost instantly, such as ketchup, and are called pseudoplastic fluids. Others such as yogurt take much longer and can become nearly solid. Many gels and colloids are thixotropic materials, exhibiting a stable form at rest but becoming fluid when agitated. Thixotropy arises because particles or structured solutes require time to organize.

<span class="mw-page-title-main">Dilatant</span> Material in which viscosity increases with the rate of shear strain

A dilatant material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid, also known by the initialism STF, is an example of a non-Newtonian fluid. This behaviour is usually not observed in pure materials, but can occur in suspensions.

In continuum mechanics, rheopecty or rheopexy is the rare property of some non-Newtonian fluids to show a time-dependent increase in viscosity ; the longer the fluid undergoes shearing force, the higher its viscosity. Rheopectic fluids, such as some lubricants, thicken or solidify when shaken. The opposite and much more common type of behaviour, in which fluids become less viscous the longer they undergo shear, is called thixotropy.

<span class="mw-page-title-main">Rheometer</span> Scientific instrument used to measure fluid flow (rheology)

A rheometer is a laboratory device used to measure the way in which a viscous fluid flows in response to applied forces. It is used for those fluids which cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. It measures the rheology of the fluid.

Rheometry generically refers to the experimental techniques used to determine the rheological properties of materials, that is the qualitative and quantitative relationships between stresses and strains and their derivatives. The techniques used are experimental. Rheometry investigates materials in relatively simple flows like steady shear flow, small amplitude oscillatory shear, and extensional flow.

<span class="mw-page-title-main">Thickening agent</span> Increases the viscosity of a liquid without altering its other properties

A thickening agent or thickener is a substance which can increase the viscosity of a liquid without substantially changing its other properties. Edible thickeners are commonly used to thicken sauces, soups, and puddings without altering their taste; thickeners are also used in paints, inks, explosives, and cosmetics.

Fluid mechanics is the branch of physics concerned with the mechanics of fluids and the forces on them. It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.

<span class="mw-page-title-main">Shear thinning</span> Non-Newtonian fluid behavior

In rheology, shear thinning is the non-Newtonian behavior of fluids whose viscosity decreases under shear strain. It is sometimes considered synonymous for pseudo-plastic behaviour, and is usually defined as excluding time-dependent effects, such as thixotropy.

<span class="mw-page-title-main">Viscosity</span> Resistance of a fluid to shear deformation

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square meter, or pascal-seconds.

Constant viscosity elastic liquids, also known as Boger fluids are elastic fluids with constant viscosity. This creates an effect in the fluid where it flows like a liquid, yet behaves like an elastic solid when stretched out. Most elastic fluids exhibit shear thinning, because they are solutions containing polymers. But Boger fluids are exceptions since they are highly dilute solutions, so dilute that shear thinning caused by the polymers can be ignored. Boger fluids are made primarily by adding a small amount of polymer to a Newtonian fluid with a high viscosity, a typical solution being polyacrylamide mixed with corn syrup. It is a simple compound to synthesize but important to the study of rheology because elastic effects and shear effects can be clearly distinguished in experiments using Boger fluids. Without Boger fluids, it was difficult to determine if a non-Newtonian effect was caused by elasticity, shear thinning, or both; non-Newtonian flow caused by elasticity was rarely identifiable. Since Boger fluids can have constant viscosity, an experiment can be done where the results of the flow rates of a Boger liquid and a Newtonian liquid with the same viscosity can be compared, and the difference in the flow rates would show the change caused by the elasticity of the Boger liquid.

<span class="mw-page-title-main">Time-dependent viscosity</span> Property of certain fluids to change viscosity over time

In continuum mechanics, time-dependent viscosity is a property of fluids whose viscosity changes as a function of time. The most common type of this is thixotropy, in which the viscosity of fluids under continuous shear decreases with time; the opposite is rheopecty, in which viscosity increases with time.

Biofluid dynamics may be considered as the discipline of biological engineering or biomedical engineering in which the fundamental principles of fluid dynamics are used to explain the mechanisms of biological flows and their interrelationships with physiological processes, in health and in diseases/disorder. It can be considered as the conjuncture of mechanical engineering and biological engineering. It spans from cells to organs, covering diverse aspects of the functionality of systemic physiology, including cardiovascular, respiratory, reproductive, urinary, musculoskeletal and neurological systems etc. Biofluid dynamics and its simulations in computational fluid dynamics (CFD) apply to both internal as well as external flows. Internal flows such as cardiovascular blood flow and respiratory airflow, and external flows such as flying and aquatic locomotion. Biological fluid Dynamics involves the study of the motion of biological fluids. It can be either circulatory system or respiratory systems. Understanding the circulatory system is one of the major areas of research. The respiratory system is very closely linked to the circulatory system and is very complex to study and understand. The study of Biofluid Dynamics is also directed towards finding solutions to some of the human body related diseases and disorders. The usefulness of the subject can also be understood by seeing the use of Biofluid Dynamics in the areas of physiology in order to explain how living things work and about their motions, in developing an understanding of the origins and development of various diseases related to human body and diagnosing them, in finding the cure for the diseases related to cardiovascular and pulmonary systems.

Peanut butter is a viscoelastic food that exhibits both solid and fluid behaviors. It consists of ground up peanuts and may contain additional additives, such as stabilizers, sugars, or salt. Its characteristic soft, spreadable texture can be further defined through rheology – the study of flow and deformation of matter, affecting texture, consistency, and mouthfeel. Specifically for peanut butter, rheology can be used to more accurately define characteristics, such as spreadability and grittiness.

References

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  7. This demonstration of oobleck is a popular subject for YouTube videos.[ which? ]
  8. 1 2 "Oobleck: The Dr. Seuss Science Experiment". instructables.com.
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